A woman holds a Syrian flag during a protest against Bashar al-Assad outside the Syrian embassy in Amman. Amnesty has accused the Syrian regime of torturing the relatives of people protesting overseas. Photograph: Majed Jaber/Reuters

The Syrian government has been accused of torturing the relatives of Syrians protesting overseas in an attempt to silence international criticism of President Bashar al-Assad's regime.

The charges are made in a report from Amnesty International – The Long Reach of the Mukhabaraat (the name of the Syrian secret police) – which details more than 30 cases of direct and indirect intimidation of activists in Canada, Chile, France, Germany, Spain, Sweden, the UK and US.

One dissident, now living in Germany, told Amnesty that his brother had been arrested, held for a month and tortured by Syrian military intelligence because of his sibling's anti-regime stance. In Sweden, another pro-reform activist said her activities on the internet and the streets of Stockholm had attracted the attention of the Syrian authorities.

At the end of May, she received a letter in Arabic using her maiden name, which warned her: "Keep quiet or neither you, nor your family in Syria is safe." Not long after, her brother was arrested in Damascus, had both his hands broken and was forced to promise that the family would disown his sister.

Anti-regime activists in several countries have reported being harassed, intimidated and even assaulted.

Five weeks ago in Paris, a 35-year-old Syrian engineer and two fellow demonstrators were attacked by a group of men and women carrying pro-Assad flags. They say they were told by French police officers that no action could be taken against two of their assailants because they held diplomatic passports. Later that night, according to the engineer, more anti-regime protesters were attacked with baseball bats by the same group.

According to the Amnesty study, the elderly parents of a US-based Syrian were badly beaten and locked in their bathroom in the city of Homs after their son – a pianist and composer – was filmed performing at a pro-reform demonstration in front of the White House. In Illinois, an expatriate Syrian activist reported receiving a menacing email after one of her Facebook friends in Syria was arrested for protesting at his university and being forced to open his account on the social network.

It read: "These words are directed at you, you agent, you traitor. Your messages have come to us … We are waiting for you to come to the airport so we can show you what is good for you and for what you are doing. We will make an example out of you."

British-based demonstrators say they have also been filmed while protesting, phoned and visited at home by Syrian embassy staff, and threatened with death. One protester said Mukhabaraat officers raided his mother's home in Damascus, asking questions about him and eventually forcing her to flee the country.

Another British-based protester, Ghias Aljundi, told the Guardian he had been called on his mobile in June by someone claiming to be from the embassy. "He said: 'Don't think you are protected. We can get you anyway. It's better for you to stop what you are doing. You are a traitor'." Aljundi added: "I didn't feel comfortable at all. I know they're not going to do anything to me, but I immediately had to call my brothers to see what was happening [in Syria].

"The regime is completely morally bankrupt and so they can do anything."

The FO is also liaising with Scotland Yard and urging demonstrators to report any evidence of harassment or other crimes by embassy staff to the Metropolitan police.

Scotland Yard said it was aware of the allegations of intimidation and is investigating a claim of harassment made on 28 August.

Amnesty is calling on the Syrian government to immediately end its harassment of protesters and their families, and is asking the international community to make sure such intimidation does not go unchecked.

"We look to host governments to act on credible allegations of abuses without waiting for formal complaints," said Neil Sammonds, Amnesty's Syrian researcher.

"Many of the people we have spoken to are too scared of what could happen to them to make formal complaints with the police. We would expect that any official found responsible for such acts should be prosecuted, or – if diplomatic immunity prevents that – asked to leave the country."

No one at the Syrian embassy in London could be reached for comment on the allegations.

Despite the apparent intimidation, UK-based Syrians are planning to stage an "I am not afraid" demonstration outside the Syrian embassy on Tuesday morning.

During the protest, they will hold placards inscribed with their names and home towns.